metric spaces; $g$-metrizable spaces; 1-sequence-covering mappings; $\sigma $-mappings; quotient mappings
In this paper, the relationships between metric spaces and $g$-metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
 P. Alexandroff: On some results concerning topological spaces and their continuous mappings
. In: Proc. Symp. Gen. Top. (Prague, 1961), 1961, pp. 41–54. MR 0145472
 Shou Lin: On sequence-covering $s$-mappings
. Adv. Math. (China) 25 (1996), 548–551. MR 1453163
 Shou Lin: $\sigma $-mappings and Alexandroff’s problems. (to appear).
 J. R. Boone and F. Siwiec: Sequentially quotient mappings
. Czechoslovak Math. J. 26 (1976), 174–182. MR 0402689
 A. V. Arhangel’skii: Mappings and spaces
. Russian Math. Surveys 21 (1966), 115–162. MR 0227950
 Y. Tanaka: $\sigma $-hereditarily closure-preserving $k$-networks and $g$-metrizability
. Proc. Amer. Math. Soc. 112 (1991), 283–290. MR 1049850
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